Chapter 14 Test 3 Computer Practice

# Chapter 14 Test 3 Computer Practice - A chain of sports...

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Unformatted text preview: A chain of sports clubs is interested in which features to offer in a new location. The CEO of the chain gathered data from existing clubs regarding the number of members, median income in the area, whether the club had a pool, and when classes were offered (morning, afternoon, night, all day). A. Give the regression equation for predicitng the number of members a new gym will have. B. Give the appropriate coefficient of determination. C. Interpret the coefficient for median income. D. Interpret the coefficient for night classes. E. Is the model valid for prediciting membership at the 5% significance level? F. Is income a useful predictor for membership? Alpha = .10 G. I s there a difference in membership between gyms that offer only morning classes and those that offer classes all day? Alpha = .05 H. Give a 95% confidence interval for the coefficient for income. I. Give a range of values for the mean membership of gyms that have a pool, medain income in the surrounding area of \$44, 880, and offer classes in the afternoon. J. Give a range of values for the membership of a gym that does not have a pool, offers classes in the morning, and has a median income in the surrounding area of \$46,924. K. Is multicollinearity a problem in your model? Justify your answer. A. Ŷ = -­‐902.991 + 0.053 X income + 434.299 X pool + 253.203 X morning + 308.593 X afternoon + 405.066 X night B. .953 C. Holding all other indpt variables constant, for an increase of \$1 in median income, selling price will increase on avg by \$.05 D. Holding all other indpt vars constant, a gym that offers night classes will have 405.066 members more on avg than one tha E. Ho: β1 = β2= β3 = β4 = β5 = 0 Ha: at least one β not = 0 F = 62.360 pvalue = 3.26 E -­‐7 There is enough evidence to conclude the model is valid for predicting membership. F. Ho: β1 = 0 Ha: β1 not = 0 T = 10.955 pvalue = 6.85E-­‐7 There is enough evidence to conclude income is a useful predictor for membership. G. Ho: β3 = 0 Ha: β3 not = 0 T = 1.092 pvalue = 0.300 There is not enough evidence to conclude there is a difference in memebership between gyms that offer only mo H. 0.043 , 0.064 I. Predicted Values for New Observations 95% 1608.2 , 2864.4 J. New Obs Fit SE Fit 95% CI 95% PI 1 2236.3 281.9 (1608.2, 2864.4) (1410.7, 3061.8)X X denotes a point that is an outlier in the predictors. Values of Predictors for New Observations New Obs income pool morning afternoon night 1 44880 1.00 0.000000 1.00 0.000000 K. No, there are no indpt variables that are highly correlated to each other. SUMMARY OUTPUT Regression Statistics Multiple R 0.984347 R Square 0.9689391 Adjusted R S0.9534087 quare Standard Error 240.43032 Observations 16 ANOVA df Regression Residual Total SS MS F Significance F 5 18032708 3606541.7 62.389639 3.261E-­‐07 10 578067.41 57806.741 15 18610776 Coefficients Standard Error t Stat Intercept -­‐902.9914 311.49941 -­‐2.898854 income 0.0533947 0.0048738 10.955408 pool 434.29865 221.27685 1.9626935 morning 253.20343 231.79863 1.0923422 afternoon 308.59336 252.49215 1.2221899 night 405.06573 197.46469 2.0513325 P-­‐value 0.0158647 6.846E-­‐07 0.0780863 0.3002996 0.2496616 0.0673579 Lower 95% -­‐1597.055 0.0425351 -­‐58.7369 -­‐263.2761 -­‐253.9942 -­‐34.91301 Upper 95% -­‐208.9274 0.0642542 927.33421 769.68297 871.18093 845.04447 members income pool 1258 32223 1479 34975 1480 43187 1701 44337 2014 52167 2271 57521 2615 58347 2632 60960 2737 62201 2810 67993 3563 68770 3765 81289 3792 83902 4069 84594 4393 86855 4787 88381 morning 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 afternoon night 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 1 pool N N N N N N N Y Y N N Y N Y Y Y n + 405.066 X night rice will increase on avg by \$.053. mbers more on avg than one that offers classes all day. tween gyms that offer only morning classes and those that offer classes all day. New Obs Fit SE Fit 95% CI 95% PI 1 1855.7 138.9 (1546.1, 2165.3) (1237.0, 2474.4) Values of Predictors for New Observations New Obs income pool morning afternoon night 1 46924 0.000000 1.00 0.000000 0.000000 95% 1237.0 , 2474.4 Lower 95.0% Upper 95.0% -­‐1597.055 -­‐208.9274 0.0425351 0.0642542 -­‐58.7369 927.33421 -­‐263.2761 769.68297 -­‐253.9942 871.18093 -­‐34.91301 845.04447 classes morning afternoon night morning all afternoon night all all morning night all night all all night ...
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